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From a cryptographic sense, what value is added from setting the domain to be the image in the mapping?

Kartik Chopra
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A one-way permutation (OWP) is more structured than a one-way function, and hence a stronger object. This makes the task of constructing higher cryptographic objects from OWPs easier and also, at times, leads to more efficient constructions. For example, consider pseudo-random generators (PRGs): it is quite straightforward to construct a PRG from a OWP; but constructing a PRG from a OWF took a lot more effort -- you can read more here.

ckamath
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    Yes. But for small domain ( e.g $\{0,1\}^{256}$ ), a public OWP is much harder to construct than a public OWF. If one has such OWP, I want to know ! Thus [I asked](https://crypto.stackexchange.com/q/54079/555). – fgrieu Dec 19 '17 at 13:56
  • That's an interesting question! – ckamath Dec 19 '17 at 15:04